Applying Abstract Argumentation Theory to Cooperative Game Theory

We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in cooperative game theory by showing that complete extensions (the grounded extension) correspond to Roth's subsolutions (respectively, the supercore). We then investigate the relationship between well-founded argumentation frameworks and convex games, where in each case the semantics (respectively, solution concepts) coincide; we prove that three-player convex games do not in general have well-founded argumentation frameworks.Comment: 15 pages, 1 tabl

Strategic Argumentation is NP-Complete

In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments. We show how to model dialogue games in a skeptical, non-monotonic formalism, and we show that the problem of deciding what move (set of rules) to play at each turn is an NP-complete problem

Abstract Games of Argumentation Strategy and Game-Theoretical Argument Strength

We define a generic notion of abstract games of argumentation strategy for (attack-only and bipolar) argumentation frameworks, which are zero-sum games whereby two players put forward sets of arguments and get a reward for their combined choices. The value of these games, in the classical game-theoretic sense, can be used to define measures of (quantitative) game-theoretic strength of arguments, which are different depending on whether either or both players have an “agenda” (i.e. an argument they want to be accepted). We show that this general scheme captures as a special instance a previous proposal in the literature (single agenda, attack-only frameworks), and seamlessly supports the definition of a spectrum of novel measures of game-theoretic strength where both players have an agenda and/or bipolar frameworks are considered. We then discuss the applicability of these instances of game-theoretic strength in different contexts and analyse their basic properties

A game-theoretic perspective on the notion of argument strength in abstract argumentation

This paper is concerned with the problem of quantifying the strength of arguments in controversial debates, which we model as abstract argumentation frameworks [Dung, 1995]. Standard approaches to abstract argumentation provide only a qualitative account of the status of arguments, whereas numerical measures of argument strength might provide a more precise evaluation of their individual status. Intuitively, the strength of an argument in a debate essentially depends on how a proponent of that argument would defend himself against the criticisms of someone opposed to the argument. Since there can be many ways of defending and attacking an opinion, we essentially conceive argument strength as an equilibrium resulting from the interactions taking place between the opinions that a proponent and an opponent of the argument could a priori embrace. More formally, we define argument strength in terms of the value of a repeated two-person zero-sum strategic game with imperfect information. Then, using the game-theoretic properties of such games and notably the von Neumann minimax theorem [Neumann, 1928], we establish and illustrate the main properties of this new argument strength measure

A Comparative Study of Ranking-based Semantics for Abstract Argumentation

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been proposed independently, often associated with some desirable properties. However, there is no comparative study which takes a broader perspective. This is what we propose in this work. We provide a general comparison of all these semantics with respect to the proposed properties. That allows to underline the differences of behavior between the existing semantics.Comment: Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI-2016), Feb 2016, Phoenix, United State

Stratified Labelings for Abstract Argumentation

We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions

Analysis of Dialogical Argumentation via Finite State Machines

Dialogical argumentation is an important cognitive activity by which agents exchange arguments and counterarguments as part of some process such as discussion, debate, persuasion and negotiation. Whilst numerous formal systems have been proposed, there is a lack of frameworks for implementing and evaluating these proposals. First-order executable logic has been proposed as a general framework for specifying and analysing dialogical argumentation. In this paper, we investigate how we can implement systems for dialogical argumentation using propositional executable logic. Our approach is to present and evaluate an algorithm that generates a finite state machine that reflects a propositional executable logic specification for a dialogical argumentation together with an initial state. We also consider how the finite state machines can be analysed, with the minimax strategy being used as an illustration of the kinds of empirical analysis that can be undertaken.Comment: 10 page

Coalitional games for abstract argumentation

International audienceIn this work we address the issue of the uncertainty faced by a user participating in multiagent debate. We propose a way to compute the relative relevance of arguments for such a user, by merging the classical argumentation framework proposed in [5] into a game theoretic coalitional setting, where the worth of a collection of arguments (opinions) can be seen as the combination of the information concerning the defeat relation and the preferences over arguments of a " user ". Via a property-driven approach, we show that the Shapley value [15] for coalitional games defined over an argumentation framework, can be applied to resume all the information about the worth of opinions into an attribution of relevance for the single arguments. We also prove that, for a large family of (coalitional) argumentation frameworks, the Shapley value can be easily computed